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The Foundations of Mathematics and Other Logical Essays

London, England: Routledge & Kegan Paul. Edited by R. B. Braithwaite (1925)

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  1. The Nature of Appearance in Kant’s Transcendentalism: A Seman- tico-Cognitive Analysis.Sergey L. Katrechko - 2018 - Kantian Journal 37 (3):41-55.
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  • Keynes's Theory of Probability and Its Relevance to His Economics: Three Theses.Allin Cottrell - 1993 - Economics and Philosophy 9 (1):25-51.
    One calls a lot of things propositions. If one sees this, then one can discard the idea Russell and Frege had that logic is a science of certain objects – propositions, functions, the logical constants – and that logic is like a natural science such as zoology and talks about these objects as zoology talks of animals. Like a natural science, it could supposedly discover certain relations. For example, Keynes claimed to discover a probability relation which was like implication, yet (...)
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  • Compositionality and Complexity in Multiple Negation.Francis Corblin - 1995 - Logic Journal of the IGPL 3 (2-3):449-471.
    This paper considers negative triggers and the interpretation of simple sentences containing more than one occurrence of those items . In the most typical interpretations those sentences have more negative expressions than negations in their semantic representation. It is first shown that this compositionality problem remains in current approaches. A principled algorithm for deriving the representation of sentences with multiple negative quantifiers in a DRT framework is then introduced. The algorithm is under the control of an on-line check-in, keeping the (...)
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  • Disciplining Qualitative Decision Exercises: Aspects of a Transempirical Protocol, I.John W. Sutherland - 1990 - Theory and Decision 28 (1):73.
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  • Speaking for Oneself: Wittgenstein on Ethics.Matthew Pianalto - 2011 - Inquiry: An Interdisciplinary Journal of Philosophy 54 (3):252-276.
    In the “Lecture on ethics”, Wittgenstein declares that ethical statements are essentially nonsense. He later told Friedrich Waismann that it is essential to “speak for oneself” on ethical matters. These comments might be taken to suggest that Wittgenstein shared an emotivist view of ethics—that one can only speak for oneself because there is no truth in ethics, only expressions of opinion (or emotions). I argue that this assimilation of Wittgenstein to emotivist thought is deeply misguided, and rests upon a serious (...)
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  • Three Letters on the Foundations of Mathematics by Frank Plumpton Ramsey†.Paolo Mancosu - forthcoming - Philosophia Mathematica.
    Summary This article presents three hitherto unpublished letters by Frank Plumpton Ramsey on the foundations of mathematics with commentary. One of the letters was sent to Abraham Fraenkel and the other two letters to Heinrich Behmann. The transcription of the letters is preceded by an account that details the extent of Ramsey's known contacts with mathematical logicians on the Continent.
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  • Are Credences Different From Beliefs?Roger Clarke & Julia Staffel - forthcoming - In Ernest Sosa, Matthias Steup, John Turri & Blake Roeber (eds.), Contemporary Debates in Epistemology, 3rd edition. Wiley-Blackwell.
    This is a three-part exchange on the relationship between belief and credence. It begins with an opening essay by Roger Clarke that argues for the claim that the notion of credence generalizes the notion of belief. Julia Staffel argues in her reply that we need to distinguish between mental states and models representing them, and that this helps us explain what it could mean that belief is a special case of credence. Roger Clarke's final essay reflects on the compatibility of (...)
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  • Evidentialist Reliabilism.Juan Comesaña - 2010 - Noûs 44 (4):571-600.
    I argue for a theory that combines elements of reliabilism and evidentialism.
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  • Probability, likelihood and support: A metamathematical approach to a system of axioms for upper and lower degrees of belief.A. I. Dale - 1976 - Philosophical Papers 5 (2):153-161.
    (1976). PROBABILITY, LIKELIHOOD AND SUPPORT: A METAMATHEMATICAL APPROACH TO A SYSTEM OF AXIOMS FOR UPPER AND LOWER DEGREES OF BELIEF. Philosophical Papers: Vol. 5, No. 2, pp. 153-161.
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  • Anaphoric attitudes.M. J. Cresswell - 1990 - Philosophical Papers 19 (1):1-18.
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  • Necessary Identity.M. J. Pendlebury - 1975 - Philosophical Papers 4 (1):12-20.
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  • Tolerance and Voluntarism.Paul Dicken - 2013 - Philosophical Papers 42 (1):25-48.
    Carnap's mature philosophy of science is an attempt to dissolve the scientific realism debate altogether as a philosophical pseudo-question. His argument depends upon a logico-semantic thesis regarding the structure of a scientific theory, and more importantly, a meta-ontological thesis regarding the explication of existence claims. The latter commits Carnap to a distinction between the analytic and the synthetic, which was allegedly refuted by Quine. The contemporary philosophy of science has therefore sought to distance itself from logico-semantic considerations, and has pursued (...)
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  • Probabilist antirealism.Igor Douven, Leon Horsten & Jan-Willem Romeijn - 2010 - Pacific Philosophical Quarterly 91 (1):38-63.
    Until now, antirealists have offered sketches of a theory of truth, at best. In this paper, we present a probabilist account of antirealist truth in some formal detail, and we assess its ability to deal with the problems that are standardly taken to beset antirealism.
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  • Generalizing Detached Self-Reference and the Semantics of Generic One.Friederike Moltmann - 2010 - Mind and Language 25 (4):440-473.
    In this paper I will give an analysis of what I call ‘generalizing detached self-reference’ within a general account of reference to the first person. With generalizing detached self-reference an agent attributes properties to a range of individuals by putting himself into their shoes, or simulating them. I will show that generalizing detached self-reference plays an important role in the semantics of natural language, in particular in the English generic one and in what syntacticians call arbitrary PRO.
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  • A Quantum-Bayesian Route to Quantum-State Space.Christopher A. Fuchs & Rüdiger Schack - 2011 - Foundations of Physics 41 (3):345-356.
    In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation (...)
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  • How Degrees of Belief Reflect Evidence.James M. Joyce - 2005 - Philosophical Perspectives 19 (1):153-179.
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  • Harms and objections.Michael McDermott - 2019 - Analysis 79 (3):436-448.
    Intuition says that choosing to create a miserable person is wrong, but choosing not to create a happy one is not; this is ‘the Asymmetry’. There is a complete theory which agrees – the ‘Harm Minimization’ theory. A well-known objection is that this theory rejects Parfit’s principle of ‘No Difference’. But No Difference has less intuitive support than the Asymmetry, and there seems to be no complete theory which agrees with both. There is, however, a more serious problem for Harm (...)
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  • Does causal descriptivism solve the problem of reference of theoretical terms?Bruno Borge - 2017 - Ideas Y Valores 66 (163):125-151.
    RESUMEN Las teorías de la referencia puramente descriptivistas o causales fracasan a la hora de dar cuenta del modo en que se fija y puede rastrearse la referencia de los términos teóricos. Psillos propuso dos versiones del descriptivismo causal que recogen argumentos presentes en defensas previas de dicha posición. Se trata de una teoría mixta que pretende solucionar el problema y acomodarse a intuiciones presentes en enfoques alternativos, como el que apela a oraciones de Ramsey. El artículo se propone mostrar (...)
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  • Russell's Schema, Not Priest's Inclosure.Gregory Landini - 2009 - History and Philosophy of Logic 30 (2):105-139.
    On investigating a theorem that Russell used in discussing paradoxes of classes, Graham Priest distills a schema and then extends it to form an Inclosure Schema, which he argues is the common structure underlying both class-theoretical paradoxes (such as that of Russell, Cantor, Burali-Forti) and the paradoxes of ?definability? (offered by Richard, König-Dixon and Berry). This article shows that Russell's theorem is not Priest's schema and questions the application of Priest's Inclosure Schema to the paradoxes of ?definability?.1 1?Special thanks to (...)
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  • Logic, Mathematics, Philosophy, Vintage Enthusiasms: Essays in Honour of John L. Bell.David DeVidi, Michael Hallett & Peter Clark (eds.) - 2011 - Dordrecht, Netherland: Springer.
    The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...)
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  • Математизирането на историята: число и битие.Vasil Penchev - 2013 - Sofia: BAS: ISSk (IPR).
    The book is a philosophical refection on the possibility of mathematical history. Are poosible models of historical phenomena so exact as those of physical ones? Mathematical models borrowed from quantum mechanics by the meditation of its interpretations are accomodated to history. The conjecture of many-variant history, alternative history, or counterfactual history is necessary for mathematical history. Conclusions about philosophy of history are inferred.
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  • Objetores de Descartes, ¿y también de Frege? Apuntes críticos al artículo “La naturaleza de las entidades matemáticas. Gassendi y Mersenne: objetores de Descartes”.Emilio Méndez Pinto - 2021 - Dianoia 66 (86):129-144.
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  • Can We Infer Our Empirical Beliefs From Our Sense Experiences?Rinita Mazumdar - 1996 - Dissertation, University of Massachusetts Amherst
    Inference is a process by which appropriate belief states get connected. Belief states are biological states in the sense that they are reentrant loops ; their intrinsic feature is recognition. In inference or reasoning the transition process between belief states is regulated by the rule of concept usage, involved in the belief state, in natural language. Like belief states experiential states are also biological states whose extrinsic feature is recognition, such that, one can have an, say, X-type experience without recognizing (...)
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  • Mental Maps1.Ben Blumson - 2011 - Philosophy and Phenomenological Research 85 (2):413-434.
    It's often hypothesized that the structure of mental representation is map-like rather than language-like. The possibility arises as a counterexample to the argument from the best explanation of productivity and systematicity to the language of thought hypothesis—the hypothesis that mental structure is compositional and recursive. In this paper, I argue that the analogy with maps does not undermine the argument, because maps and language have the same kind of compositional and recursive structure.
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  • Decision theory, intelligent planning and counterfactuals.Michael John Shaffer - 2008 - Minds and Machines 19 (1):61-92.
    The ontology of decision theory has been subject to considerable debate in the past, and discussion of just how we ought to view decision problems has revealed more than one interesting problem, as well as suggested some novel modifications of classical decision theory. In this paper it will be argued that Bayesian, or evidential, decision-theoretic characterizations of decision situations fail to adequately account for knowledge concerning the causal connections between acts, states, and outcomes in decision situations, and so they are (...)
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  • Unphilosophical probability.Sandy L. Zabell - 1981 - Behavioral and Brain Sciences 4 (3):358-359.
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  • The rule of succession.Sandy L. Zabell - 1989 - Erkenntnis 31 (2-3):283 - 321.
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  • In defense of a constructive, information-based approach to decision theory.M. R. Yilmaz - 1997 - Theory and Decision 43 (1):21-44.
    Since the middle of this century, the dominant prescriptive approach to decision theory has been a deductive viewpoint which is concerned with axioms of rational preference and their consequences. After summarizing important problems with the preference primitive, this paper argues for a constructive approach in which information is the foundation for decision-making. This approach poses comparability of uncertain acts as a question rather than an assumption. It is argued that, in general, neither preference nor subjective probability can be assumed given, (...)
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  • The Metaphysics of Degrees.René Woudenberg & Rik Peels - 2018 - European Journal of Philosophy 26 (1):46-65.
    Degree-sentences, i.e. sentences that seem to refer to things that allow of degrees, are widely used both inside and outside of philosophy, even though the metaphysics of degrees is much of an untrodden field. This paper aims to fill this lacuna by addressing the following four questions: [A] Is there some one thing, such that it is degree sensitive? [B] Are there things x, y, and z that stand in a certain relation to each other, viz. the relation that x (...)
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  • What did Frege take Russell to have proved?John Woods - 2019 - Synthese 198 (4):3949-3977.
    In 1902 there arrived in Jena a letter from Russell laying out a proof that shattered Frege’s confidence in logicism, which is widely taken to be the doctrine according to which every truth of arithmetic is re-expressible without relevant loss as a provable truth about a purely logical object. Frege was persuaded that Russell had exposed a pathology in logicism, which faced him with the task of examining its symptoms, diagnosing its cause, assessing its seriousness, arriving at a treatment option, (...)
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  • Sellars on Bradley's 'paradox'.James Jeffrey Wilkin - 1979 - Philosophical Studies 36 (1):51 - 59.
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  • Dynamic semantics versus dynamic propositionalism.Malte Willer - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy.
    Una Stojnić's Context and Coherence: The Logic and Grammar of Prominence offers a series of interesting criticisms of the classical dynamic paradigm in natural language semantics and offers a sophisticated alternative outlook, one that does recognize a dynamic, context change inducing dimension of meaning but at the same preserves the idea that (declarative) utterances express propositions in context. The purpose of this note is to set the record straight: existing dynamic analyses of modals and conditionals compare favorably with Stojnić's dynamic (...)
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  • The iterative solution to paradoxes for propositions.Bruno Whittle - 2022 - Philosophical Studies 180 (5-6):1623-1650.
    This paper argues that we should solve paradoxes for propositions (such as the Russell–Myhill paradox) in essentially the same way that we solve Russellian paradoxes for sets. That is, the standard, iterative approach to sets is extended to include properties, and then the resulting hierarchy of sets and properties is used to construct propositions. Propositions on this account are structured in the sense of mirroring the sentences that express them, and they would seem to serve the needs of philosophers of (...)
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  • Cohen on contraposition.N. E. Wetherick - 1981 - Behavioral and Brain Sciences 4 (3):358-358.
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  • Realism and Behaviourism.Alan Weir - 1986 - Dialectica 40 (3):167-200.
    SummaryMany contemporary philosophers of language believe that realist metaphysics and a beha‐viouristic approach to language are incompatible, debate centring on which is to be given up. In this paper I argue that no incompatibility has been shown to exist. In the first section I attempt to give both a characterization of, and an argument for, behaviourism. Then I attempt to characterize realism more generally than is often done, evaluating the work of Dummett, Quine, Putnam and Wittgenstein, as recently interpreted, in (...)
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  • Competence, performance, and ignorance.Robert W. Weisberg - 1981 - Behavioral and Brain Sciences 4 (3):356-358.
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  • Indicative and subjunctive conditionals.Brian Weatherson - 2001 - Philosophical Quarterly 51 (203):200-216.
    This paper presents a new theory of the truth conditions for indicative conditionals. The theory allows us to give a fairly unified account of the semantics for indicative and subjunctive conditionals, though there remains a distinction between the two classes. Put simply, the idea behind the theory is that the distinction between the indicative and the subjunctive parallels the distinction between the necessary and the a priori. Since that distinction is best understood formally using the resources of two-dimensional modal logic, (...)
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  • Metaphysics and the advancement of science.J. W. N. Watkins - 1975 - British Journal for the Philosophy of Science 26 (2):91-121.
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  • The importance of cognitive illusions.Peter Wason - 1981 - Behavioral and Brain Sciences 4 (3):356-356.
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  • Sometimes the world is not enough: The pursuit of explanatory laws in a Humean world.Barry Ward - 2003 - Pacific Philosophical Quarterly 84 (2):175–197.
    A novel motivation for a Humean projectivist construal of our concept of scientific law is provided. The analysis is partially developed and used to explain intuitions that are problematic for a Humean reductionist construal of lawhood. A possible non-Humean rejoinder is discussed and rejected. In an appendix, further intuitions that are problematic for Humean reductionists are explained projectively.
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  • An Indexical Theory of Conditionals.Ken Warmbrōd - 1981 - Dialogue 20 (4):644-664.
    Language theorists have recently come to have an increasing appreciation for the fact that context contributes heavily in determining our interpretation of what is said. Indeed, it now seems clear that no complete understanding of a natural language is possible without some account of the way in which context affects our interpretation of discourse. In this paper, I will attempt to explore one facet of the language – context relationship, namely, the relation between conditionals and context. The first part of (...)
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  • The Nature of Properties: Causal Essentialism and Quidditism.Jennifer Wang - 2016 - Philosophy Compass 11 (3):168-176.
    Properties seem to play an important role in causal relations. But philosophers disagree over whether or not properties play their causal or nomic roles essentially. Causal essentialists say that they do, while quidditists deny it. This article surveys these two views, as well as views that try to find a middle ground.
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  • The Essences of Fundamental Properties.Jennifer Wang - 2019 - Metaphysics 2 (1):40-54.
    There is a puzzle concerning the essences of fundamental entities that arises from considerations about essence, on one hand, and fundamentality, on the other. The Essence-Dependence Link (EDL) says that if x figures in the essence of y, then y is dependent upon x. EDL is prima facie plausible in many cases, especially those involving derivative entities. But consider the property negative charge. A negatively charged object exhibits certain behaviors that a positively charged object does not: it moves away from (...)
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  • Separating marginal utility and probabilistic risk aversion.Peter Wakker - 1994 - Theory and Decision 36 (1):1-44.
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  • Principia ’s Second Edition [review of Bernard Linsky, The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition ]. [REVIEW]Russell Wahl - 2013 - Russell: The Journal of Bertrand Russell Studies 33 (1):59-67.
    In lieu of an abstract, here is a brief excerpt of the content:russell: the Journal of Bertrand Russell Studies n.s. 33 (summer 2013): 59–94 The Bertrand Russell Research Centre, McMaster U. issn 0036–01631; online 1913–8032 oeviews PRINCIPIA’S SECOND EDITION Russell Wahl English and Philosophy / Idaho State U. Pocatello, id 83209, usa [email protected] Bernard Linsky. The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition. Cambridge: Cambridge U. P., 2011. Pp. vii, 407; 2 plates. isbn: 978-1-10700-327-9. (...)
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  • The Axiom of Reducibility.Russell Wahl - 2011 - Russell: The Journal of Bertrand Russell Studies 31 (1).
    The axiom of reducibility plays an important role in the logic of Principia Mathematica, but has generally been condemned as an ad hoc non-logical axiom which was added simply because the ramified type theory without it would not yield all the required theorems. In this paper I examine the status of the axiom of reducibility. Whether the axiom can plausibly be included as a logical axiom will depend in no small part on the understanding of propositional functions. If we understand (...)
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  • Independent forebrain and brainstem controls for arousal and sleep.Jaime R. Villablanca - 1981 - Behavioral and Brain Sciences 4 (3):494-496.
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  • Ramsey on judgment: The theory of "facts and propositions".John M. Vickers - 2004 - Dialectica 58 (4):499–516.
    Ramsey's “Facts and Propositions” is terse, allusive, and dense. The paper is far from easy to understand. The present essay is an effort, largely following Brian Loar's account,1 to say what Ramsey's goal is, to spell out what he took to be the means to accomplish it, and to show how those means, at least in the terms of F&P, cannot accomplish that end. I also contrast Loar's own account of judgment, explicitly modeled on Ramsey's view, with the latter. The (...)
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  • Prudence and extensionality in theories of preference and value.J. M. Vickers - 1995 - Theory and Decision 39 (3):267-299.
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  • Logique et gnoséologie dans les Principia Mathematica et Inquiry into Meaning and Truth chez Russell.Denis Vernant - 2020 - Revue de Synthèse 141 (1-2):85-105.
    Résumé Procédant à une relecture de l’article de Jules Vuillemin « Difficultés logiques et problèmes philosophiques dans les Principia Mathematica de Russell », nous montrerons d’abord qu’effectivement la logique pure des Principia ne peut s’appliquer qu’à requérir des engagements existentiels sur des objets logico-mathématiques. Puis, en prolongeant les réflexions de Vuillemin, nous établirons que dans An Inquiry into Meaning and Truth Russell élabore une logique du langage ordinaire pour rendre compte à la fois de notre usage du langage et de (...)
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